It's a lot more than that, it's:

• Knowing what parts to buy, I don't think most average people can cite every piece in a desktop
• Selecting parts that are compatible, try plug-and-play an AMD CPU on an Intel MOBO.
• Selecting parts that fit the chassis you selected, unless you went with a full ATX that's a concern.

Now that you bought the components:

• Knowing to ground yourself before doing anything, currently I'm getting static shocks daily where I live, if I didn't know about this I could very easily fry a RAM by picking it up wrong.
• Cable management is not easy, most cheaper chassis don't have enough or dedicated space for it.
• Correct amount of thermal paste is something lots of people get wrong.
• Some pieces require strength to lock in place, others break if you even look at them sideways.

Now that you've assembled everything:

• Installing OS
• Installing drivers
• Installing Steam
• Depending on your OS and controller of choice pairing controller and getting it to work could be difficult

I'm not saying that assembling a computer is hard, but is definitely far from plug-and-play, and not something I would recommend for someone without technical knowledge who just wants something to play games.

That's the wording a lot of other people would use, I'd say. I wouldn't be able to put together a PC, and most people I know are like that. I have maybe two cousins that can. But we'd probably all agree that plug-and-play means that you buy something and it works just like that. For example, a refrigerator is likely plug and play, because you don't expect to have to put together the components to make it work. You just plug it in and it works.